Efficient Bias Robust Cross Section Factor Models

Abstract

This paper introduces a theory based robust regression estimator, called the mOpt estimator, that minimizes the maximum bias with respect to a Tukey-Huber mixture model that includes a standard linear regression model with normally distribution errors as a special case, but also allows for a small fraction of unrestricted fat-tailed and skewed non-normal distribution variations from the standard model. The estimator has a very intuitive weighted least squares interpretation based on a data-dependent weight function that is equal to zero for robustly scaled prediction residuals that are larger in magnitude than 3.0, and thereby rejects outliers. We apply the robust regression method to single factor and multiple factor cross-section models for Size, BM, Beta and EP factors, and find that the robust regression results reverse the Fama-French 1992 (FF92) conclusions concerning the significance of the Size, Beta and EP factors. The difference in our results and those of FF92 is that the robust regression rejects approximately 4% to 5% of outliers, most of which, but not all, occur for microcap stocks, with smallcap stocks also having some influential outliers, and even largecaps have a few. We strongly recommend standard use of the mOpt estimator as an important complement to least squares for empirical asset pricing research, as well as for quantitative finance applications in general.